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90 lines
2.5 KiB
C++
90 lines
2.5 KiB
C++
/*
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boost header: numeric/odeint/gram_schmitt.hpp
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Copyright 2011-2013 Karsten Ahnert
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Copyright 2011 Mario Mulansky
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
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#define BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
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#include <boost/throw_exception.hpp>
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#include <iterator>
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#include <algorithm>
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#include <numeric>
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namespace boost {
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namespace numeric {
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namespace odeint {
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template< class Iterator , class T >
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void normalize( Iterator first , Iterator last , T norm )
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{
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while( first != last ) *first++ /= norm;
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}
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template< class Iterator , class T >
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void substract_vector( Iterator first1 , Iterator last1 ,
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Iterator first2 , T val )
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{
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while( first1 != last1 ) *first1++ -= val * ( *first2++ );
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}
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template< size_t num_of_lyap , class StateType , class LyapType >
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void gram_schmidt( StateType &x , LyapType &lyap , size_t n )
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{
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if( !num_of_lyap ) return;
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if( ptrdiff_t( ( num_of_lyap + 1 ) * n ) != std::distance( x.begin() , x.end() ) )
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BOOST_THROW_EXCEPTION( std::domain_error( "renormalization() : size of state does not match the number of lyapunov exponents." ) );
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typedef typename StateType::value_type value_type;
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typedef typename StateType::iterator iterator;
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value_type norm[num_of_lyap];
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value_type tmp[num_of_lyap];
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iterator first = x.begin() + n;
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iterator beg1 = first , end1 = first + n ;
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std::fill( norm , norm+num_of_lyap , 0.0 );
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// normalize first vector
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norm[0] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
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normalize( beg1 , end1 , norm[0] );
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beg1 += n;
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end1 += n;
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for( size_t j=1 ; j<num_of_lyap ; ++j , beg1+=n , end1+=n )
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{
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for( size_t k=0 ; k<j ; ++k )
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{
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tmp[k] = std::inner_product( beg1 , end1 , first + k*n , 0.0 );
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// clog << j << " " << k << " " << tmp[k] << "\n";
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}
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for( size_t k=0 ; k<j ; ++k )
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substract_vector( beg1 , end1 , first + k*n , tmp[k] );
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// normalize j-th vector
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norm[j] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
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// clog << j << " " << norm[j] << "\n";
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normalize( beg1 , end1 , norm[j] );
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}
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for( size_t j=0 ; j<num_of_lyap ; j++ )
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lyap[j] += log( norm[j] );
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}
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} // namespace odeint
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} // namespace numeric
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} // namespace boost
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#endif //BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
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